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NUMBER SENSE ROUTINES: DESIGNED TO BE USED AS CLASS STARTERS TO ENGAGE YOUR STUDENTS, FOSTER MATHEMATICAL DISCOURSE, AND CREATE CLASSROOM COMMUNITY. CLICK HERE TO LEARN ABOUT THE DIFFERENT TYPES OF ROUTINES.

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UPDATE 3/17/19: The updated cards can be found in this post (Multiplication Subitizing Cards: An Upgrade to Building Fluency)

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Learning basic facts through tricks or a mnemonic song lead students down a path of memorization, not understanding. I previously discussed the idea of conceptual development here. When students practice their multiplication facts, they're expected to move from concrete to abstract too quickly. This takes time!!!

Moving too quickly forces memorization and avoids any possibility of multiplicative thinking. First students are asked to model 3 rows of 6 using colored tiles...

Then after a day or two of exploring arrays, students are magically expected to remember that...

Intensions are good but strategy development is the key underpinning of automaticity. In the past I've asked myself the following questions:

When do students practice multiplication that's not written as AxB? (for the purpose of automaticity)

When/how is multiplicative reasoning fostered?

When do multiplication strategies become automatized?

When do number strategies become number knowledge?

My answer to all 4 questions....I use multiplication subitizing cards with my daughter whose in 2nd grade so I figured I'd videotape and share.

My takeaways:

It's easy to identify which facts she's comfortable with and has automatized.

At 1:15- she demonstrates how she used multiplicative thinking for 6×6.

At 2:00- she could use her understanding of the commutative property for multiplication to build fluency. She was quickly is able to recognize that 7×5=35 at 1 minute, but it took some time to figure out 5×7. She owns this strategy for addition so I'm waiting for it to click with multiplication....no rush:-)

At 2:20- I missed a fact when she was wrong (doh!)

At 2:48 and 3:55 she explains her multiplicative reasoning.

5 minutes spent purposefully building fluency and I gained so much information about my daughter. The great thing is that it works for every 8 year old...even the ones in your school.

Disclaimer: I didn't create the cards and don't know who did but they deserve a virtual math hug! If you know who did please let me know so I can give proper attribution!

Cheers!

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Subitizing to Foster Multiplicative Thinking

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UPDATE 3/17/19: The updated cards can be found in this post (Multiplication Subitizing Cards: An Upgrade to Building Fluency) ---------- Learning basic facts through tricks or a mnemonic song lead students down a path of memorization, not understanding. I previously discussed the idea of conceptual development here.

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Where’s Poly? An Exploration in Geo-Dotting

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Download the Resource What’s geo-dotting? I have no clue but that’s what I’m calling this lesson. We started by asking, “What do you notice?” Our favori…

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Estimation 180 (more intermediate appropriate)

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Estimation 180 (more intermediate appropriate)

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ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together.

Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.

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How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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Over 15 years ago, I began using Imposter Sets in my math classroom. Imposter Sets frequently produce rich, insightful discussion about important math concepts. Students readily embrace the mystery of Imposter Sets. Classroom discussions are frequently characterized by investigation, exploration, and wonder. Those are powerful responses to a strategy that is actually very simple to use.

Recently I was asked to share more about Imposter Sets. What are they? How can they be used in the classroom?

You'll find several resources below. I just recorded a video explaining Imposter Sets, and there is also a PDF ready for you to download. I hope your classroom will be filled with a sense of investigation and wonder.
Click Here to Download Sample Imposter Sets PDF Enjoy the video! Using Imposter Sets in the Classroom
If you would like to learn about more animated math instructional strategies, you'll find additional posts listed on the left, including the "I'm on a Learning Mission" all-time most popular post The Animated Multiplication Table.

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Math Imposter Sets (with Video and PDF) - Steve Wyborney's Blog: I'm on a Learning Mission.

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Over 15 years ago, I began using Imposter Sets in my math classroom. Imposter Sets frequently produce rich, insightful discussion about important math

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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20 Days of Number Sense & Rich Math Talk - for all grades from K-12. That is the goal of this series. Entirely new, exclusive content fills this post in a ready-to-use format that will allow you to deeply explore 4 rich math routines.

By downloading each day, you can have a clear pathway to presenting rich number sense and math discourse opportunities to your students.

Additionally, each day contains multiple levels, so that a 2nd grade teacher, a 5th grade teacher, and a high school teacher can all be using the same file - and can all have access to other grade levels. The opportunities to differentiate across levels abound in this series as well as the opportunities to see into other grade levels from K-12.

Update: If you would like to read about Kathy Iwanicki's journey into 20 Days of Number Sense & Rich Math Talk, you can find her blog post here. Thank you for sharing your story, Kathy!

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.
Quick Access to Days 1-5 Simply click on the blue link to download the file. Quick Access to Days 6-10 Simply click on the blue link to download the file. Quick Access to Days 11-15 Simply click on the blue link to download the file. Quick Access to Days 16-20 Simply click on the blue link to download the file. Quick Access to the solutions for the Advanced Cube Conversations
Quick Access to the Cube Conversations Book The Cube Conversations Printable PDF Description of 20 Days of Number Sense & Rich Math Talk (K-12) Days 1-5
The Answers to the Advanced Cube Conversations Tasks (Days 16-20)
I've opened the series with a brand new set of Estimation Clipboards. The Estimation Clipboard strategy is a very invitational way to draw students into rich number sense discussions as it layers in more and more context and continues to provide students with estimation opportunities. The Estimation Clipboard strategy is also where a very important math instructional reality becomes abundantly clear: Writing is a powerful springboard into math discourse. As students WRITE their estimates (particularly for images 3 & 4) the math talk in your classroom will become very rich. You'll find the power in the pattern of (1) students estimating (2) writing their estimate (3) explaining what their estimate is, and why they chose it. Then right before each reveal, your classroom will become very quite in anticipation of the reveal. Don't be surprised if there is a lot cheering as the answers are revealed.
Days 6-10
Days 1-5 have set the stage with The Estimation Clipboard. Not only have the 20 Days of Number Sense and Rich Math Talk begun, but both students and teachers have detected the power of invitations, estimation, writing, sharing their ideas aloud, and experiencing the joy and wonder of math.

Day 1 - The Estimation Clipboard

Day 2 - The Estimation Clipboard

Day 3 - The Estimation Clipboard

Day 4 - The Estimation Clipboard

Day 5 - The Estimation Clipboard

After the highly invitational nature of the Estimation Clipboard, opportunities to richly explore numbers continue in the Splat! images which are all brand new - and are all designed to work in both PowerPoint and Google Slides (just like everything else in this series - so feel free to use either one).

Ranging from Splats through 10 through Fraction Splats! and now including 10 of the most challenging Splats! that I have ever publicly released, your students will have very rich opportunities to lean into number sense and richly discuss their mathematical thinking while also hearing from other students. They will be able to see and explore multiple strategies for decomposing numbers, adding, subtracting, multiplying, dividing, and connecting many concepts together.

Since every day includes materials across a wide range of grade levels, there is also a really good opportunity to take a look at content from other grade levels and offer even more challenges to your students.

Let's take a closer look at each of the Splat! levels include in 20 Days of Number Sense and Rich Math Talk.

Splat! Level A includes numbers through 10 and is ideal for grades K-1. In these sequences the dots appear so that students can count them. Then, when you click, the total number appears in the corner. On the next click, the SPLAT appears and covers some of the dots. The immediate question is, "How many dots are under the Splat?" You will be amazed at how many different ways students see this, solve this, and even how they mentally move the dots around to decompose and make sense of the numbers. If you look at the images below, you'll see that some of the Splats separate the visible numbers and create a Part-Part-Part-Whole scenario. Splat Level A appears in all 5 days.

Splat! Level B includes numbers through 10 and is ideal for grades 1-2. It also provides the first example of a grade level (kindergarten) that may recognize the opportunity to venture to higher levels. Just like in Level A, the first click introduces the dots, the next click brings in the Splat and the question, and then the Number Sense and Rich Math Talk begins. When I use numbers through 20 in the classroom, I sometimes quickly move through the counting step by saying, "Here are some dots. There are 19 of them. This is the Splat!" I find that counting so many dots can slow down the opportunities that the Splat introduces. Of course, counting is critical, and so is finding many different ways to count, so at other times I spend more time on a variety of grouping and counting methods. The reality is that there are so many opportunities in these slides that you have many opportunities to focus on a wide range of concepts.

The images in Splat! Level C are some of the most wide-ranging images I have ever worked with. It offers opportunities across so many grade levels. I've labeled it as primarily matching grades 2-5, but I've seen it used very effectively in many grade levels. Level C is where multiplication and division begin to play a much stronger role. While students in younger grades may access the image above (the one that shows 14) by adding, subtracting, grouping, counting on, repeatedly adding 3 to 5, or repeatedly subtracting 5 from 14, I've seen other strategies across grade levels. For example, fourth grade students sometimes view it as 14 ÷ 3 with a remainder of 5. Likewise, high school students have viewed is as 3x + 5 = 14. Imagine the power of the conversation among the students across those grade levels!

A very interesting option opens up in Splat! Level D. In the images above you are seeing the first of the reveal clicks. In the moment before this - when all of the Splats are opaque, and none of the dots beneath the can be seen - students approach a new question, which is "What could the total be?" In the first image above, before it is revealed that each Splat is covering 3 dots, students find themselves working with the concepts that the total must be 3 more than a multiple of 3, so the total must be a multiple of 3. However, in the second picture above (again before the first Splat is revealed like you see in the picture) students can see that the total is unknown, that there are 4 visible dots, and that there are 7 splats. By rule, each splat is covering the same number. So students can work with the concepts such as that total must be 4 more than a multiple of 7. As the identify possible totals, they can see that it could be 4, 11, 18, 25, ... Then when you choose to reveal the value of a Splat by clicking, you'll see a single Splat turn transparent (which is what you see in the images above) and the students can determine what the total number of dots is. You may expect the students to use multiplication to do so, and many will, but they will also surprise you with a wide number of strategies that you may never have expected. They are showcasing both Number Sense & Rich Math Talk!

Level E is a favorite of many teachers. In this level, all of the whole dots and all of the fractional parts of a dot can be seen. Then when you click, the Splat appears, and covers some of the whole dots and fractional parts. The immediate question becomes, "What is the value beneath the Splat?" I am amazed at how students approach these questions.

Level F is similar to the previous level with one exception. While, Level E allow the students to see all of the images before the Splat appeared, Level F simply presents the total, the Splat, and the visible parts of the total all at the same time. Students once again bring very impressive insights into the conversation. It's Number Sense and Rich Math Talk and the way that students contribute to one another's insights is eye-opening.

Level G allows the students to see the all of the whole numbers and all of the fractions on the screen and gives the students the opportunity to determine the total. When you click the total will appear. Then, with the next click, multiple Splats will appear on the screen. By rule, each of the Splats is covering the same number (the same value), although those numbers may be represented in different ways. The students task is to determine the value of the Splats (not the specific pieces) under each Splat.

Level H is similar Level G, accept in Level H the Splats all appear at the very beginning, so the first image the students see are just line the ones that are showing above. The question is, "What is the value of each Splat?" Within Level, H (on days 9 & 10), I have included 10 of the most challenging Splat questions I have ever publicly released.

Day 6 - Exclusive Splat Sequences Days 11-15

Day 7 - Exclusive Splat Sequences Day 11 - Exclusive Esti-Mysteries Days 16-20

Day 12 - Exclusive Esti-Mysteries

Day 13 - Exclusive Esti-Mysteries

Day 14 - Exclusive Esti-Mysteries

Day 15 - Exclusive Esti-Mysteries

Day 8 - Exclusive Splat Sequences

Day 16 - Exclusive Cube Conversations

Day 17 - Exclusive Cube Conversations

Day 18 - Exclusive Cube Conversations

Day 19 - Exclusive Cube Conversations

Day 20 - Exclusive Cube Conversations

Day 9 - Exclusive Splat Sequences

Day 10 - Exclusive Splat Sequences
Remember that I've written slides for ALL levels on EVERY day. Download the day you are on, find the level you want to work with, and let your students exercise their Number Sense and engage in Rich Math Talk.

Also, consider challenging your students by trying out 2-3 slides from another level.

Exclusive Esti-Mysteries

15 brand new Esti-Mysteries fill these 5 days, and each day includes 3 different levels, ranging from kindergarten to advanced math concepts. As a bonus, the first 3 Esti-Mysteries include appearing charts on the screen. Additionally, 2 of the Esti-Mysteries include multiple perspectives and hidden clues that can be found in the 2nd image.

Esti-Mysteries strongly call upon number sense and promote rich math talk while also giving students rich opportunities to COMBINE estimation with a range of math concepts in the context of rich math talk. Students will be discussing their estimates - much like in the first 5 days when the work with the Estimation Clipboard - but will also be looking carefully at math concepts and seeing how those concepts are interrelated.

Exclusive Cube Conversations

The highly visual cube conversations strategy is used in the final 5 days to promote number sense and rich math talk. In addition to brand new Cube Conversations Images, the downloadable set of matching pages will give students clear opportunities to annotate and describe their insights to one another.

As with all other days in this series, there is a very good opportunity to see into other grade level bands, and this can be use to differentiate content, challenge students, and promote even deeper number sense and rich math talk.

At the end of each day there is also a challenging task, which is placed in the highest grade band. The printable PDF includes 2 different versions of each task. One version includes 4 copies so that students will have an opportunity to try out 4 different entry points into the task, while the other page simply offers a larger, easier-to-use version of the image.

The beginning level of Cube Conversations provides very good opportunities to visualize and decompose small numbers in a wide variety of ways. The middle image shown above is animated to showcase 3 different ways that students may see how to decompose the shape. Likely, they will find many more than the 3 examples, but the animated examples typically provide a nice momentum and a clear invitation to seek out many different ways to decompose the number. Then another image appears (like the third one shown above) with 4 additional copies below it so that ideas can be shared with the entire class. As with all levels, every image is also available on the downloadable PDF so that each student can decompose the images on their own and then share their ideas with one another.

Deepening Cube Conversations (grades 2-5) introduce some layers of complexity that allow students to work with additional concepts, such as visualizing sets in multiple ways, visualizing shapes that overlap (so the overlapping cubes may need to be subtracted), and shapes that appear to have holes in them.

The 2nd image above shows layers that will appear when you click (although on the slide you download the images will all be in a single location on the slide). If you look at the middle image closely, you will see how the image has been decomposed into 9 + 3 groups of 3, then 2 groups of 5 and a group of 3 and 5 groups of 1. Still focusing on the blue and yellow shape in the middle image above, you can see why students describe it many ways. For example, a student might say, "I see 3 groups of 5 in the blue and yellow image." If you look carefully, you'll also see 3 groups of 5.

Then moving the the last image in the center picture above (the image which is red, yellow, and blue in the bottom right corner) you can see how a student might say, "I see three groups of five plus three more - but I see it in a different way." Remember, that is just the example page and it is followed by the wide open opportunity presented on the next slide. When you look at the third picture above you can see how a student might describe two groups of 9, two groups of 8, or even 2 groups of 7 while other students describe groups of 2, 3, or 5. You may also hear that a student sees a 25 minus two groups of 4 and 2 groups of 1. The possibilities go on and on as your provide students with rich opportunities to explore Number Sense and to explore and describe their insights together.

The routine continues - but at a deeper level - in Textured Cube Conversations. Remember, every level is available on every day in this blog post, and all content in 20 Days of Number Sense and Rich Math Talk is exclusive to this post.

The first image will present a structure, several examples of how the structure can be visually decomposed, and will finally reveal the number of unit cubes. Then a new image will appear with 4 opportunities on the bottom of the screen for students to show their thinking to each other.

All of the Cube Conversations images are available in PDF format so that you can provide each student with their own copy to annotate - and then to share their ideas with one another.

Advanced Cube Conversations will feel very much like a rich task. Two of the Advanced Cube Conversations are illustrated in the pictures above.

The thinking that comes from these tasks is tremendous!

On the downloadable PDF you will find a page with a large image of the structure an an additional page that provides 4 smaller versions of that picture so that students will have multiple opportunities to try out a variety of entry points.

In each case the question is, "This structure is composed of how many unit cubes?"

I hope you enjoy 20 Days of Number Sense & Rich Math Talk. If you do, please leave a comment. You can even share who is using it. Perhaps we'll see some classrooms from around the world leaving comments like, "We are using #20DaysNS in Hunters, Washington!"

As always, you can find me on Twitter @stevewyborney

I'll be keeping an eye on #20DaysNS on Twitter.

I wish you well as you work with your students and give them opportunities to develop their numbers sense and engage in rich math talk.

All my best,

Steve

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20 Days of Number Sense & Rich Math Talk (K-12) - Steve Wyborney's Blog: I'm on a Learning Mission.

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20 Days of Number Sense & Rich Math Talk - for all grades from K-12. That is the goal of this series. Entirely new, exclusive content fills this post in a

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AASD Student Centered Intervention Template

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AASD Student Centered Intervention Template

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Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

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Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

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With the implementation of new standards, assessments, and (for some) new curriculum, teachers are feeling bogged down and yet left out on their own to make sense of it all.

Gain knowledge of how kids learn math so that you can confidently close your textbook and do fun lessons that meet your students where they are.

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Build Math Minds | Learn to LOVE Teaching Math

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With the implementation of new standards, assessments, and (for some) new curriculum, teachers are feeling bogged down and yet left out on their own to make sense of it all. Gain knowledge of how kids learn math so that you can confidently close your textbook and do fun lessons that meet your students where they are.

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*Why Do Number Talks? Ruth Parker,MEC

*Implementing Number Talks- Helpful Hints

*Building Facility with Number Talks- Grade Level Expectations- Ruth Parker

Number Talks-combinations to 20, place value These number talks are focused on learning the number combinations to 20, and place value understanding. Developed by Barb Rauert,Math Recovery Instructor

Number Talks-Multiplication

K-2 Routines, 3-5 Routines, Middles School Routines

Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5 Author: Sherry Parish

I t Makes Sense!: Using Ten-frames to Build Number Sense,Melissa Conklin

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Why Do Number Talks? Ruth Parker,MEC *Implementing Number Talks- Helpful Hints *Building Facility with Number Talks- Grade Level Expectations- Ruth Parker Number Talks-combinations to 20, place value These number talks are focused on learning the number combinations to 20, and place value understanding.

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Math Number Talks K 5 - Lessons - Tes Teach

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Video 1.Video 2.Video 3.Video 4.Video 5.Video 6.Video 7.Video 8.Video 9.Video 10.Video 11.Video 12.Anchor Chart.NT Printables.Hand Signals.Sherry Parrish: Number Talks: Building Numerical Reasoning

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Our KNP (Kentucky Numeracy Project) team proves that collective brain power is greater than the sum of the individuals brain power.

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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100 Subitizing Slides & 10 Challenge Patterns - Steve Wyborney’s Blog: I’m on a Learning Mission.

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I have a new resource for you. 100 Subitizing Slides & 10 Challenge Patterns.

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K-3 Splat

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Steve Wyborney's Blog: I'm on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

This post includes 50 (fifty!) free, downloadable PowerPoint math lessons!

Watch the video, download some (or all) of the lessons, and experience what happens when you unleash this resource in your classroom!

I've been excited to click the Publish button on this post for several weeks! It's time!
UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

Splat Through 10
How many dots are under the Splat?

Splat Through 20
How many dots are under the Splat?

Multiple Splats
(Note: Splats that are the same color must cover the same number.)
Splat 3.1 - multiple splats Splat 3.2 - multiple splats Splat 3.3 - multiple splats Splat 3.4 - multiple splats Splat 3.5 - multiple splats
Instant Multiple Splat
(Note: An additional feature of this level is the opportunity to ask, "What could the total be?")

Splat 4.1 - Instant Multiple Splats Splat 4.2 - Instant Multiple Splats Splat 4.3 - Instant Multiple Splats Splat 4.4 - Instant Multiple Splats Splat 4.5 - Instant Multiple Splats
2-Color Splat
(Splats of different colors must have different values.)

Splat 5.1 2-color Splat Splat 5.2 2-color Splat Splat 5.3 2-color Splat Splat 5.4 2-color Splat Splat 5.5 2-color Splat Splat 6.2 Instant 2-color Splat Splat 6.3 Instant 2-color Splat Splat 6.4 Instant 2-color Splat Splat 6.5 Instant 2-color Splat
Instant 2-Variable Splat
(Splats of different colors must have different values. Splats of the same color must have the same value.)
Splat 7.1 Instant 2-variable Splat Splat 7.2 Instant 2-variable Splat Splat 7.3 Instant 2-variable Splat Splat 7.4 Instant 2-variable Splat Splat 7.5 Instant 2-variable Splat
Number Splat
(Note: Only the numbers circled on the screen may be used.)
Splat 8.1 - Number Splat Splat 8.2 - Number Splat Splat 8.3 - Number Splat Splat 8.4 - Number Splat Splat 8.5 - Number Splat Splat 9.1 - Instant Number Splat Splat 9.2 - Instant Number Splat Splat 9.3 - Instant Number Splat Splat 9.4 - Instant Number Splat Splat 9.5 - Instant Number Splat
Instant Number Splat with 2 Variables
(Note: Only the numbers circled on the screen may be used, and Splats of different colors must have different values.)
Splat 10.1 - Instant 2-Variable Number Splat Splat 10.2 - Instant 2-Variable Number Splat Splat 10.3 - Instant 2-Variable Number Splat Splat 10.4 - Instant 2-Variable Number Splat Splat 10.5 - Instant 2-Variable Number Splat
NOTE: I wrote each of these lessons using PowerPoint, so I recommend playing them in PowerPoint. If you do not have PowerPoint, you may want to download the PowerPoint viewer so that you can play the lessons.

UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
Other Posts and Resources Which May Be of Interest Tiled Area Questions The Maze Hundreds Chart
Introducing Cube Connectors
Provide Massive Space to Notice
Primary Tile Questions
3 Powerful Tile Strategies (and 40 new downloadable pages)
Please take a moment to subscribe to the blog so you'll be notified each time new resources are posted!

I would treasure hearing about your experiences using Splat! to promote number sense in your classroom!

All my best,
Steve

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Splat! - Steve Wyborney's Blog: I'm on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

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Steve Wyborney's Blog: I'm on a Learning Mission.

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Here is a new resource for you: The Number Concept Map.

While there are many different ways this resource could be used in the classroom, I've provided a recording below to detail how you might gather representations in your classroom community, and also to show how you might use those representations to look for connections among the ideas once that have been gathered.

I hope the video and the downloadable Number Concept Map will be helpful in your classroom. I would love to hear about your classroom journey!
You can download the blank number concept map here.
If you are interested in other animated posts, you might want to take a look at " The Animated Multiplication Table."

You may also be interested in Math Imposter Sets (with video and PDF).

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The Number Concept Map (Video and PDF) - Steve Wyborney's Blog: I'm on a Learning Mission.

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Here is a new resource for you: The Number Concept Map. While there are many different ways this resource could be used in the classroom, I've provided a recording below to detail how you might gather representations in your classroom community, and also to show how you might use those representations to look for...

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51 Esti-Mysteries - Steve Wyborney's Blog: I'm on a Learning Mission.

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Grade 5

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Copy of Copy of Math Workshop Lesson Plan_ Task and Share 

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Math Workshop Lesson Plan_ Guided Math 2 (1)

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Math workshop template with a focus lesson 

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Math workshop template with a focus lesson 

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Games and Activities | Dr Paul Swan Maths

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Last century I wrote a "Best of Math Math World" - a collection of the best ideas, activities and games from Math Math World, a puzzle booklet that I still write for the Mathematical Association of Western Australia.

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Resources for number talks K-6

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Teacher: Time for our morning Number Talk.
Everyone consider this question. (She writes 9 + 17 on the board).
(A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.)
If you get more answers, show me by holding up more fingers. (She waits for 30 seconds. Several students are holding up multiple fingers, though many have just a thumb.
The teacher is noting to see if anyone hasn't solved the problem-this is a great opportunity for formative assessment.
Finally, she begins calling on students for their answers, starting with those who have only one solution.)

Teacher: Lucy?
Lucy: 26. (Teacher writes 26 on the board.)

Teacher: Charles?
Charles: 107 (Teacher writes 107 on the board.)

Teacher: Michelle?
Michelle: 25. (Teacher writes 25 on the board.)

Teacher: Any other answers? (No one has any.)
Who would like to explain how they got their answer? Tyrone?
(The teacher records what the students write as they explain.)

Tyrone: I know that 9 + 7 is 16, and then I added another 10 to get 26.
Sarah: 10 + 17 is 27, and 10 is 1 more than 9, so 9 + 17 must be 26.
Charles: 9 + 1 is 10, and then you put a 7 after, so it's 107.
Lucy: I counted one by one, but I just realized that I miscounted.
I agree with 26
(Teacher crosses out 25 and replaces it with 26.)
Sam: I respectfully disagree with Charles.
You can't add the 9 + 1 because the 1 stands for 10.
Charles: But that's how you add. I did it right.
(Teacher lets conversation continue until class consensus, or near-consensus, is reached.
Meanwhile, she's noting where students are in their understanding of place value and addition.)

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Teacher: Time for our morning Number Talk. Everyone consider this question. (She writes 9 + 17 on the board). (A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.)

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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Steve Wyborney's Blog: I'm on a Learning Mission.

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Here is a new resource for you: The Number Concept Map.

While there are many different ways this resource could be used in the classroom, I've provided a recording below to detail how you might gather representations in your classroom community, and also to show how you might use those representations to look for connections among the ideas once that have been gathered.

I hope the video and the downloadable Number Concept Map will be helpful in your classroom. I would love to hear about your classroom journey!
You can download the blank number concept map here.
If you are interested in other animated posts, you might want to take a look at " The Animated Multiplication Table."

You may also be interested in Math Imposter Sets (with video and PDF).

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The Number Concept Map (Video and PDF) - Steve Wyborney's Blog: I'm on a Learning Mission.

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Here is a new resource for you: The Number Concept Map. While there are many different ways this resource could be used in the classroom, I've provided a recording below to detail how you might gather representations in your classroom community, and also to show how you might use those representations to look for...

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These Geometric Subitizing Cards have been in beta the past two years.

I asked our buddy Joe Schwartz to take them for a test drive last spring and he reported back. Joe's all in.

How do they work? Let's play...

Last week I took them for another spin in some kindergarten classes. Here's two examples of how it went and we're only 2 months into the school year.

Last year I captured me playing cards with my girls. Here's me playing with my kindergartner.

Here's me playing with my 3rd grader.

Your turn.

Take these cards and give them a try. If you need some ideas how to use them you might want to check out this task card. I plan to share my thoughts about Geometric Subitizing in a future post but for now I just want you to go and play. The only thing I ask is that you report back and offer feedback.

How did it go?

How can we make them better?

Any other ways we could use them?

What am I missing?

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Geometric Subitizing: A Different Kind of Number Talk

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Download the Resource These Geometric Subitizing Cards have been in beta the past two years. I asked our buddy Joe Schwartz to take them for a test drive last spring and he rep...

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Same But Different is a powerful routine for use in math classrooms. The images can be used for teaching a way of thinking: grayscale thinking, categorical thinking; helping students to build a network of ideas and an approach for learning and thinking about mathematics.

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Steve Wyborney's Blog: I'm on a Learning Mission.

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The Estimation Clipboard is a set of 40 lessons that each include 4 highly similar images. Each image provides an invitation to estimation. Then as new images are introduced, the students' context and intrigue will grow - and so will their excitement.

The Estimation Clipboard series is arranged in 4 different levels. Watch the video, download the lessons, and try The Estimation Clipboard in your class. You may be very surprised by what is about to happen...

Keep watching The Estimation Clipboard as new images, new levels, and new combinations will be added to this post on an ongoing basis.

UPDATE: I'm now posting the lessons in bundles. Each bundle includes 4 sets. Here is a picture of a Bundle download. So when you download a bundle, you'll have the option of using 1 set each day for four days or using multiple sets in a single day.
Bundle 2 - (Sets 5, 6, 7, & 8) More to come soon!!! I'll continue to post all 40 sets throughout the next several days! Other Posts and Resources Which May Be of Interest
Splat! (over 140,000 free lessons downloads in 2017!)

The Fraction Splat! Series (with 20 more downloadable lessons) is now available!

Cube Conversations (80 downloadable, animated lessons)
Tiled Area Questions Primary Tile Questions The Maze Hundreds Chart
Thank you for visiting!

All my best,

Steve

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The Estimation Clipboard is a set of 40 lessons that each include 4 highly similar images. Each image provides an invitation to estimation. Then as new images are introduced, the students' context and intrigue will grow - and so will their excitement. The Estimation Clipboard series is arranged in 4 different levels.

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Steve Wyborney's Blog: I'm on a Learning Mission.

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I made multiplication table using and went on to discover some very interesting relationships within the table.

You will see several here. Click here to download the table. (After downloading, your first step will be to click the multiplication symbol to clear the table.)

Other posts that may interest you:

You may also be interested in viewing and downloading The Green Light Hundreds Chart.

See the updated video: Is This Claim Always True? A powerful post to use in your classroom.

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The Animated Multiplication Table - Steve Wyborney's Blog: I'm on a Learning Mission.

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I made multiplication table using PowerPoint and went on to discover some very interesting relationships within the table. You will see several here. Click here to download the table. (After downloading, your first step will be to click the multiplication symbol to clear the table.) Other posts that may interest you: The Maze Hundreds Chart...

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Printable games with a deck of cards K-6

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Printable games with a deck of cards K-6